dev/fittingPolynomial_lowOrder.R

In ffeng23/ADASPR: An R package to characterize the distributed affinities in a multi-ligand system

##R code to empirical verify exponential expansion
##
## y=exp(kx) <=> y=1+kx+(kx)^2/2!+(kx)^3/3!+(kx)^4/4!+(kx)^5/5!+....
##

x<-c(0:100)
degree<-3
fc<-factorial(c(1:degree))
k<- -1
xpoly<-poly(x*k,degree=degree,raw=T)

#####=======>note about poly
##poly is a function to calculate the polynomial format for the input
###in this case we have x =c(1,2,3,4,5,6,7,8,9,10). you can think of this 
##as 10 different concentration
# by calling poly with raw=TRUE, we got 
##[1] 1^1, 1^2,1^3, 1^4   #for the first conc=1 with degree up to 4
#@[2] 2^1, 2^2, 2^3, 2^4   #for the scond conc=2 with degree up to 4
##[3] 3^1,3^2, 3^3, 3^4  #for the third conc=3 with degree up to 4
##......
##......
#to get the full polynomial expression, we need to add x^0 terms to the matrix
#by calling cbind(xpoly, rep(1,dim(xpoly)[1]))


y<-exp(k*x)

y_poly<-rep(0,length(x))
for(i in c(1:length(x)))
{
y_poly[i]<-sum(xpoly[i,]/fc)+1
}


plot(x,y, log="", main="fitting exponential with polynomial")
 
lines(x,y_poly, col=2, lty=2 )
legend(5,0.8, c("exponential exp(-x)","polynomial with degree of 200"), col=c(1,2), pch=c(1,-1), lty=c(-1,2))

## start doing polynomial fitting of exponential to see how far we need to go with degrees
#fitpoly<-lm(y~poly(x,degree=4, raw=TRUE), weights= 1/factorial(floor(x + 0.1)))

lm.ne<-lm(formula = y ~ poly(x, degree = degree, raw = TRUE), 
	#weights = 1/factorial(floor(x + 0.1))
	weights=1/exp(x)
	)
y.we<-y+rnorm(length(y),0,0.04)
 lines(x,y.we,col=3)

lm.we<-lm(formula = y.we ~ poly(x, degree = degree, raw = TRUE), 
	#weights = 1/factorial(floor(x + 0.1))
	weights=1/exp(x)
	)